After watching a three-minute video by Cristobal Vila featuring geometric images that seamlessly transform into a nautilus, a sunflower, and the wings of a dragonfly, readers may be curious about the explicit mathematical connection between nature and mathematical topics such as the Fibonacci numbers, the golden ratio, and geometry. Reading the blog post only raises more questions and reinforces the notion that this connection is mysterious and perhaps beyond the reader. Hopefully the lack of explanation will only spur readers to dig deeper, and the puzzles presented will offer hands-on ways to explore some of the ideas in the post. But passages like "Finally here’s a truly paradoxically mystical fact about the golden ratio. Since phi is irrational, it cannot be a ratio. So where does the 'ratio' in Golden Ratio come from? Go figure! (For all eternity…)" contribute to the stereotype of mathematics as magical and unapproachable.

In contrast, a look at videographer Vila's site will shed considerable light on the mathematics in the post. Too bad no link to this site is apparent in Mutalik's post. Perhaps the reason for this oversight is that several of the answers to Mutalik's true/false questions are contained in Vila's page. The most surprising bit of myth concerning the Golden Ratio is that the "Golden Spiral" is truly the shape of a nautilus. While close to the shape of a nautilus, the Golden Spiral is not a true representation. Vila acknowledges that he realized this only after he had finished his animation, which he had to fudge a bit.

In 2009, researchers from Cornell University combed over 400 studies addressing the lack of representation of women in STEM fields. Rather than finding a lack of natural ability amongst women, they found that women who qualify for mathematics-based jobs often qualify for careers in other fields as well and prefer those careers in the long run. Indeed, while women earn approximately half of all bachelor's degrees in mathematics, they earn only 27% of the doctoral degrees awarded in mathematics. Although the reasons for this preference are not clear, a set of studies completed in 2010 suggests that when thinking about romance women tend to both downplay their interest in and spend less time engaging in mathematical subjects. Blogger and psychologist Heidi Grant Halvoroso infers that romantic goals may be an unconscious obstacle for women whose mathematical abilities match or exceed their male counterparts'. The studies in question evaluated both male and female participants' interests in mathematics. For example, men and women viewed romantic images and were then asked to rate their interest in mathematics-related topics. Unlike women, men did not show any change in the level of interest in mathematical topics after seeing the romantic images. But Halvoroso posits that men probably are not immune to the influence of romance. They may inhibit stereotypically "feminine" characteristics in an effort to attract others. The author also writes "As a former chemistry major who ultimately turned to psychology, this research has certainly given me a lot to chew on."

News media in the U.S. and India picked up the White House announcement of the 2011 National Medal of Science awardees. Among the winners are two mathematicians: Richard Tapia, Rice University, and Srinivasa R.S. Varadhan, New York University's Courant Institute of Mathematical Sciences. Tapia is honored "for his pioneering and fundamental contributions in optimization theory and numerical analysis and for his dedication and sustained efforts in fostering diversity and excellence in mathematics and science education." Varadhan is receiving the National Medal of Science "for his work in probability theory, especially his work on large deviations from expected random behavior, which has revolutionized this field of study during the second half of the twentieth century and become a cornerstone of both pure and applied probability. The mathematical insights he developed have been applied in diverse fields including quantum field theory, population dynamics, finance, econometrics, and traffic engineering."

The Houston Chronicle article notes that Tapia's "research into numerical optimization previously led to his election to the National Academy of Engineering, but he is best known for his efforts to recruit more women and minorities into the sciences," and "the son of Mexican immigrants, Tapia was raised in Los Angeles and was the first in his family to attend college." (See the Rice University press release.) Lakshman writes in TheHindu that the award to Varadhan (and two other scientists receiving the National Medal of Technology and Innovation) "is a testament to the role that Indian-Americans continue to play in deepening the United States' advances in science and technology." (See the NYU press release.)

Ruhr University statisticians Holger Dette, Axel Bücher and Stanislav Volgushev have developed a new analytical method that may calculate the probability of such extreme events as the recent simultaneous failure of traditional investment strategy and collapse of all forms of investment. "Up to now, when statisticians estimated the probabilities of extreme events, they usually calculated with dependencies between the outliers [the smallest part of a data set] of statistical series. That means they ignore the dependencies of the bulk of the relevant data set... Sometimes these data would falsify the result." Bücher explains the solution to the problem: "Our work provides a decision aid as to whether it is better to use the full range of data and not only the outliers. If all the data are relevant, then they should all be included. However, this is not always the case. Sometimes these data would falsify the result." The article notes that "the researchers used the copula function for the evaluation." Volgushev explains, "This is a complicated, multi-dimensional function, which characterizes stochastic dependencies between the data. With this aid, a few years ago we might have noticed that many little termites were nibbling their way into the wooden foundation of the global financial market, whilst we were on the lookout for large predators." Their paper, ""New estimators of the Pickands dependence function and a test for extreme-value dependence," is published in the Annals of Statistics.

Anderson writes that "Investment decisions are no longer being made by financiers, but increasingly by PhD mathematicians and the immensely complex computer programs they devise." Mathematics had previously played a role in risk management but now its influence has extended to "make money, not just to stop losing it." Computers monitor market movements as well as trading trends, and buy and sell based on algorithms, in a process called high-frequency trading. More than 2/3 of all share trades in the U.S. are done this way. Some companies even use artificial intelligence to adapt their programmed strategies. As you might expect, the computers and algorithms aren't perfect. Last May during the Flash Crash, the Dow fell 700 points in less than five minutes because the algorithms were reinforcing one another through feedback loops and selling with abandon. The market bounced back after about 30 minutes when the algorithms were manually overridden. Some say that this was a one-time occurrence but others blame the algorithms for the massive sell-offs in 2008. A UK study found that algorithmic trading helped reduce costs and did not harm overall market efficiency.

In this article, Angela Watercutter reviews the recently released movie Moneyball, based upon the story of how the Oakland Athletics became a winning team in 2002 due to the application of statistical analysis. The method, called "sabermetrics," comes to the Oakland A's front office after general manager Billy Beane hires math whiz Peter Brand. Although Brand is an amalgamation of people, the results in the movie basically match the real story. In the movie, "Beane knows he can't win with a payroll that's a fraction of a marquee team's budget, so Brand teaches him (and his scouts) how to use their money to buy hits and runs [measured by players' on-base percentages] as opposed to baseball stars. In the real world, Beane's revolutionary move altered the way people thought about baseball." Watercutter enjoys this "cerebral sports drama," calling it "a PG-13 sports movie for wonks who thought card-counting was the most interesting part of Rain Man," as well as "a math movie for sports fans who want to see a group of underdogs do well." [Editor's Note: This is assuming that watching the real-life performances of the Tampa Bay Rays and Arizona Diamondbacks isn't enough.]

To deal with budget cuts of up to 15% over the next few years--part of Conservative Prime Minister David Cameron's massive austerity package passed last summer--the Engineering and Physical Sciences Research Council, the funding body for physical sciences in the UK, has initiated a wholescale restructuring of its funding priorities. While you can't expect UK scientists to be happy about these funding cuts, what has them up in arms is the EPSRC's micromanagement of scientific research, with new priorities that don't reflect the input of UK researchers, and ignore the way fundamental science works.

Perhaps the most egregious offense is in mathematics: This July, the EPSRC halted all fellowship funding in fields outside of probability and applied statistics. Since then, David Delpy and Philippa Hemmings, the chief executive and head of mathematical sciences at EPSRC, have received letters of protest from the London Mathematical Society (LMS), the Royal Society, and the international review board whose recommendations the EPSRC solicited. Now, 20 top UK mathematicians--including four Fields Medalists and SIAM president Lloyd Trefethen--have gone over their heads, sending a letter of protest directly to Cameron. This letter insists on the unity of mathematics, saying "it is foolhardy to claim that one part of mathematics is the only useful one," pointing out that "as any subject becomes better understood, it becomes more quantitative, so that the role of mathematics becomes more important," and warning "if the EPSRC continues this policy, British mathematics will face mediocrity in a decade." As Angus MacIntyre, president of the LMS, put it: "The challenge is not to choose which areas should receive more focused support but within areas or preferably within the subject as a whole to give preference to those lines of research which currently are judged to be of greatest value."

A team of two biologists--Carl T. Bergstrom and Jevin D. West (University of Washington)--and one physicist--Martin Rosvall (University of Umeå, Sweden)--are using math to create visualizations and maps of scholarly literature. Howard likens their work to "Google Maps of scholarship" that can help researchers locate active areas of research and uncover previously unknown connections between their fields and others. The team uses information theory and network analysis to create a mapping equation and algorithm to reveal patterns in published literature. According to Howard, "The work builds off the thinking behind the Eigenfactor score, a method of assessing journals' relative influence that Mr. Bergstrom and Mr. West unveiled in 2007." Their method, which assigns higher weights to high-profiile journals like Nature, is more sophisticated than the widely-used impact factor. The team plans to make some of their tools publicly available in the fall. The image here represents strength of connections between different subjects based on the entire collection of journals at JSTOR. The stronger connections, evidenced by more citations between journals in the subjects, are represented by wider lines. See some of the JSTOR data map that is available now.

Science Friday host Ira Flatow talks to author Steven Levy about his new book In the Plex: How Google Thinks, Works, and Shapes Our Lives and his thoughts on Google's future role in the communications world. Most of the math occurs near the beginning and end of the interview. Levy begins with Google founder Larry Page's idea to rank websites based on the number of times they appear as links in other sites, an idea borrowed from academia's practice of valuing papers based on the number of times they are referenced. (See David Austin's Feature Column on Google's PageRank algorithm.) Using this principle, Page and co-founder Sergey Brin built a search engine that not only combed the links of the entire World Wide Web but also "learned" from users' searches in order to continuously improve how well the search results match the user's goal. Levy discusses Page's friendship with former Apple CEO Steve Jobs, which soured when Google expanded into Apple's territory by purchasing Android, and he predicts that Google's next move will be acquisition of a large broadband provider. Levy also highlights Google's foray into Facebook's social networking field as an attempt to acquire the enormous amount of personal data available.

Three statistics graduate students--pictured left to right: James Beguah Odei, Anvar Suyundikov, and Abbass Sharif--took part in saving a motorcyclist trapped underneath a burning car after a crash near the Utah State University’s math department in Logan. The trio joined other bystanders in lifting the burning car that was atop of Brandon Wright and dragging him from underneath it. This incredible incident was caught on video, seeing is believing. Photo by James Odei.

Educator Mariandl Hufford sounds off about recently marketed t-shirts whose slogans emphasize girls' beauty over brains, such as Forever 21's "Allergic to Algebra" shirt and J.C. Penney's "I am too pretty for homework so my brother has to do it for me." Hufford recalls a confident, sassy six-year-old girl she observed earlier that year and underscores the importance of working with young girls to ensure they maintain their self-assuredness as they grow up, including the ability to recognize and challenge the negative messages of degrading t-shirts. Time News Feed sheds a bit more light on public opinion of the Forever 21 t-shirt, highlighting the shirt's message that being beautiful is more important than getting good grades and doing well at math, and that prettiness provides an excuse for poor performance.

Over the weekend of September 11th, a memorial in New York City was dedicated to those killed 10 years earlier during the terror attacks on the World Trade Center (WTC) and the Pentagon, as well as the seven victims of the 1993 WTC bombing. While the arrangement of the 2,983 victims' names around the two memorial pools may appear random, in fact, Matson writes, the placement of names "reflects thousands of complex interpersonal relationships forged before the attacks and, on at least one occasion, during the immediate aftermath." Memorial planners "solicited requests from victims' loved ones for 'meaningful adjacencies'?names that should appear together on the memorial."

The large number of requests for interlocking adjacencies, some very complex, led the planners to use a complex algorithm built by media design firm Local Projects and software artist Jer Thorp. The first part of the algorithm built clusters of names, the largest containing some 70 names from the requests. "A second, space-filling algorithm takes those puzzle pieces and fits them into place within the confines of the 76 bronze panels enclosing each memorial pool." Finally, "organizational requirements imposed a nested, overarching system for the placement of names." For example, those who were killed in the North Tower are memorialized in the North Tower memorial, and names are grouped by company. Local Projects principal Jake Barton describes the arrangement as one showing both a "complex, human web of meaning," while at the same time preserving the chaos and randomness behind their deaths.

Much has been made of the counterintuitive, and even incomprehensible, nature of quantum mechanics. But scientists in psychology, economics, and computer science--investigators in a new field known as quantum interactions--are finding that the mathematics of quantum theory are better suited to explaining aspects of human reasoning than traditional logic. For example, humans routinely violate what is known as the "sure thing" principle. This principle says that if you hold a preference in two distinct situations, you should hold the same preference when your situation is unknown, but this is not always true: people may prefer to play a second round of a gambling game whether they win or lose the first, but not if they are unaware of the first round's outcome.

Economist Jerome Busemeyer and psychologist Emanual Pothos have shown that this seemingly paradoxical behavior can be explained in the same way as the interference observed in double-slit experiments, when particles passing through two slits at different times interact. Physicist Diederik Aerts has shown that similar "quantum effects" can account for the fuzziness of conceptual categories--the fact that people may not assign an object like a painting to a general category like "home furnishings or furniture," even when they've already assigned it to the subcategory "home furnishings." And the context-dependence of the uncertainty principle--the fact that measuring the state of a quantum object can actually change its state--may be related to the context-dependence of meaning in human language. Indeed, such quantum context-dependence is already being used to improve web searches, and computer scientist Dominic Widdows and his colleagues have used it to produce novel associations between concepts in the biomedical sciences which have already led to new research. None of which is to say that quantum mechanics is operating in our brains--it may simply be that quantum-type logic has evolved as a more effective way to make decisions, given time constraints and the presence of uncertainty.